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Keck Telescope Seismic Upgrade Design Support - Progress Report

Frank KanAndrew Sarawit4 May 2011(Revised 5 May 2011)

Purpose

• Review seismic upgrade requirements and specifications• Perform preliminary feasibility study for new seismic

restraint system to operate within 11 mm travel.

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Governing Building Code

• The latest governing building code is the Hawaii County Code 2005 Edition as amended and updated with Supplement 11. The Hawaii County Code adopted the UBC 1991 with amendment to modify the seismic zone to zone 4.

• There is also the Hawaii State Building Code 2010 which adopted the IBC 2006. Some counties have adopted this Hawaii State Building Code 2010. However, Hawaii County is not one of them.

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Design Spectra

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UBC 1991, Zone 4, Soil Type 3

UBC 1991, Zone 4, Soil Type 2

IBC 2006, Site Class D

Natural Vibration Period (sec)

Acc

ele

ratio

n (

g)

Comments on requirements and specifications

• Rare Earthquakes– Requirement: The telescope shall become fully operational after a Zone 4

or less seismic event in less than 3 days. A Rare Earthquake in a Zone 4 region is defined as 10% probability of exceedance in 50 years. The USGS peak ground accelerations for this probability at Mauna Kea is 0.4 g’s.

– Comment: The requirement of 3 days is very stringent. This typically would be in weeks. Usually for a “Rare Earthquake”, we design for “Life Safety” instead of “Immediate Occupancy” performance level. We recommend performing a cost/performance trade study to see if a feasible system can be develop to meet this requirement.

• Very Rare Earthquakes– Requirement: The telescope shall not collapse in a “Very Rare Earthquake”

defined as 2% probability of exceedance in 50 years. The peak ground acceleration for this probability is 1.2 g’s.

– Comment: 1.2g is too high. The peak ground acceleration based on 1998 data Uniform Hazard Spectrum (UHS) for 2% probability of exceedance in 50 years is 0.76g and for 10% probability of exceedance in 50 years is 0.49g. However, the IBC 2006 decided to use 0.6g as Maximum Considered Earthquake and 0.4g as Design Earthquake instead.

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Preliminary Two DOF Analysis – Parameters from Design Report in 1987

• Objective: Compute telescope Stiffness, K2

• Input Parameter:– Total weight of structure, during design = 430 kip (195 metric ton)– Weight of Elevation Structure, W2 = 172 kip (Estimate, 40% of total) – Weight of Yoke, W1 = 258 kip– Support Bracket Stiffness, k1 = 4.2 x 105 kip/in based on recent FEA of

support bracket; from Shawn Callahan.• Target Frequencies, 1987 design report:

– Mode 1: 1st Global Translation = 4.04 Hz– Mode 2: 2nd Global Translation = 7.76 Hz

• Results:– Telescope Stiffness, k2 = 5.6 x 105 kip/in.– Frequencies: Mode 1 = 2.89 Hz,

Mode 2 = 7.79 Hz– Mode 1 frequency can be increase by

increasing k2 but this would also significantly increase Mode 2 frequency.

– Results suggest that the flexibility of the seismic restraint may not have been included in the 1987 design analysis.

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m2 = W1/g

m1 = W2/g

k1

k2

Preliminary Two DOF Analysis – As-Is Condition

• Objective: Revise weights to current best estimate values and compute peak displacement and acceleration response.

• Input Parameter:

– Total weight of structure = 780 kip (354 metric ton)

– Weight of Elevation Structure, W2 = 240 kip

– Weight of Yoke, W1 = 540 kip

– Support Bracket Stiffness, k1 = 4.2 x 105 kip/in. from Shawn Callahan

– Telescope Stiffness , k2 = 5.6 x 105 kip/in.

– Design spectra: UBC 1991, Soil Type 2, Zone 4, 5% damping

• Results:

– Frequencies: Mode 1 = 2.20 Hz, Mode 2 = 5.97 Hz

– Spectra acceleration: Mode 1 = 1.0 g, Mode 2 = 1.0 g

– Peak displacement response: m1 = 47 mm, m2 = 59 mm

– Peak acceleration response: m1 = 0.92 g, m2 = 1.17 g

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Preliminary Two DOF Analysis - As-Is but with Increased Damping

• Objective: Compute peak displacement and acceleration response for system with 20% damping.

• Input Parameter:

– Design spectra: UBC 1991, Soil Type 2, Zone 4, 20% damping. Use median amplification factors under the "A" column in Table 1 of Newmark & Hall (1982) to obtain the scale factors to convert the 5% damped to 20% damped spectra. The conversion factor obtain is 1.8

• Results:

– Frequencies: Mode 1 = 2.20 Hz, Mode 2 = 5.97 Hz

– Spectra acceleration: Mode 1 = 0.55 g, Mode 2 = 0.55 g

– Peak displacement response: m1 = 26 mm, m2 = 33 mm

– Peak acceleration response: m1 = 0.51 g, m2 = 0.65 g

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Preliminary Two DOF Analysis – As-Is but with Increased Bracket Support Stiffness

• Objective: Compute bracket stiffness that would limit travel to 11 mm.

• Input Parameter:

– Peak displacement response: m1 = 11 mm

– UBC 1991, Soil Type 2, Zone 4, 5% damping design spectra

• Results:

– Support Bracket Stiffness, k1 = 15.1 x 105 kip/in. (3.6 times current system)

– Frequencies: Mode 1 = 3.64 Hz, Mode 2 = 6.86 Hz

– Spectra acceleration: Mode 1 = 0.98 g, Mode 2 = 1.0 g

– Peak displacement response: m1 = 11 mm, m2 = 26 mm

– Peak acceleration response: m1 = 0.71 g, m2 = 1.45 g > 1.2 g

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Preliminary Conclusions

• The preliminary two DOF analysis performed in this study uses estimated masses and stiffnesses therefore it can only give very rough estimates of the dynamic response.

• From the two DOF analysis of the As-Is conditions, we estimate that the maximum travel distance due to design earthquake would be 47 mm which is significantly more than the allowable 11 mm. This result is consistent with the damage experienced in the 2006 earthquake. (Need to confirm PGA of 2006 earthquake at site)

• Current design cannot be easily modified to have very high damping as there is limited travel distance, and increasing the damping alone cannot reduce the travel to be less than 11 mm. A 20% damped system will have travel distance of 26 mm.

• Increasing the stiffness of the support bracket by a factor 3.6 would reduce the travel distance to 11 mm but this would increase the peak acceleration in the elevation structure by 24% (from 1.17g to 1.45g).

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Preliminary Recommendations

• It appears there are two design options:

– Option 1: Increase the system damping

– Option 2: Increase the stiffness of seismic restraint

• Option 1 is very difficult to achieve because of the limited travel distance.

• Option 2 would increase accelerations in the elevation structure which may not be acceptable for this project. Also, one need to check the stiffness of the yoke. In the current system, the seismic restraints are probably the most flexible component. However, once they are stiffened, the yoke flexibility most be important.

• A combination of the two options might work but would require a more detail dynamic analysis to better predict the responses.

• We also recommend that we still investigate the feasibility of modifying the current system to allow for more travel distance. With more travel distance, the seismic restraint could be less stiff and possibly be designed with less damping.

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